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Encryption is the act of encoding messages. The secrecy provided by encryption is required for secure messages for electronic banking and other financial transactions, as well as many other legitimate data communications. (It is also, of course, useful for spies, criminals, and terrorists.) To send a secret message, you would use a key to encrypt (encode) the message before sending it. A key is simply some pattern of digits used to guide the encryption algorithm. The receiver of the message would then use the key to decrypt (decode) the message at the other end.
In public key encryption schemes, there are two keys. The first key, called the public key, is used to encrypt the message. The other key, the private key, is used to decrypt. Importantly, the public key cannot be used to decrypt the message, only to encrypt. For example, if you wanted to send your bank a confidential message, you would first obtain the bank's public key. This would be easy to get, since it's public. Using the public key, you would encrypt the message and transmit it to the bank. The bank would then use its private key to decrypt the message it received.
An example of an encryption program, which is freely available, is PGP (TM) http://web.mit.edu/pgp/"Pretty Good (TM) Privacy".
The United States National Security Agency has opposed the development of reasonable standards for encryption from the beginning. The U. S. government has also restricted the export of strong encryption technology. More recently, it has sought to promote "key escrow" arrangements whereby the government would keep, in effect, a spare key to everybody's encryption programs. Would you trust the government with your private key? Should you also keep a spare key to your house at the police station?